The semicontinuity conjecture for minimal log discrepancies

Let $X$ be a normal $\Q$-Gorenstein variety over an algebraically closed field of characteristic $0$, and let $Y$ be a formal $\R$-linear combination of proper closed subschemes of $X$ with positive coefficients. For a closed point $x\in X$, write

$$\mld(x;X,Y)=\inf_E\{a_E(X,Y):c_X(E)\subset\{x\}\}.$$

The semicontinuity conjecture for minimal log discrepancies. The function

$$x\mapsto \mld(x;X,Y)$$

is lower-semicontinuous on the closed points of $X$. The conjecture concerns the variation of singularities in algebraic families and is a central open problem in the theory of minimal log discrepancies. The source gives no resolution status for this statement.